I want to plot parts of this function, y = tanh(x y^2). I have been able to plot the function but I want to see just some particular parts. I am a beginner to mathematica. I have attached an image of the function. Please I need suggestions on how I can plot it.

The part of the function I want to plot can be described as below;

if |x| < x_c then x=0

if |x|>x_c then y = {upper branch of the bifurcation}

with x_c = 2.016.